Simplify the following expression: $y = \dfrac{-4k^2 + 12k + 72}{k - 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ y =\dfrac{-4(k^2 - 3k - 18)}{k - 6} $ Then we factor the remaining polynomial: $k^2 {-3}k {-18} $ ${-6} + {3} = {-3}$ ${-6} \times {3} = {-18}$ $ (k {-6}) (k + {3}) $ This gives us a factored expression: $\dfrac{-4(k {-6}) (k + {3})}{k - 6}$ We can divide the numerator and denominator by $(k + 6)$ on condition that $k \neq 6$ Therefore $y = -4(k + 3); k \neq 6$